Abstract: We studied  the kraus operator decomposition corresponding to incoherent quantum operations and strictly incoherent quantum operations  by means of operator algebra and matrix theory. Firstly, we gave the equivalence conditions of bounded linear operators as incoherent operators and the concrete forms of incoherent operators, and gave the method  of characterizing incoherent quantum operations with incoherent operators. Secondly,  we gave the concrete forms of strongly incoherent operators and the method of characterizing  strictly incoherent quantum operations with strongly incoherent operators, and gave the relationship between strictly incoherent quantum operations and incoherent quantum operations.

Key words: incoherent operator, strictly incoherent operator, incoherent quantum operation, strongly incoherent quantum operation